Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C132 · Schur multiplier (H2) = C13 |
| direct product | C5×C132×D9 |
| unambiguous semidirect product | C9⋊(C2×C5×C132) |
| Fitting, Hall | C5×C9×C132 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C5×C132 |
| Hall | C9×C132 ⋊ C2×C5 |
| Hall | C5×C9 ⋊ C2×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C132 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C5×C132 |
| Frattini | C3 | C5×D3×C132 |
| Fitting | C5×C9×C132 | C2 |
| socle | C3×C5×C132 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C5×C132 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
5070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C13×D9×D13, C5×D9×C13⋊D13, D5×C132×D9, … |
| maximal normal subgroup of | C5×C13×D9×D13, C5×D9×C13⋊D13, D5×C132×D9, … |
| maximal quotient of | C5×C132×Dic9, C2×C5×C132×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 61);